It's not inherently 'anti-government'.
Their are many different possible forms of government. The one people are most familar with now is what is known as 'State Government'.
Modern state government is largely a European invention, although it's descendent of fuedal and caste systems that are common throughout Asia and some other parts of the world. State government did not dominate the planet until towards the end of the 18th century with the industrial revolution. This allowed the European empires to mechanize their military and colonize areas of the planet that were not easily accessible to them prior to that and impose their form of government on the rest of the interior of the continents. Now the colonies and empires are dead, but the legacy of their governmental style remains in the form of constitutional republics that now virtually all modern state governments claim to be.
State government is a form of government that is made up of a centralized beaucratic authority with control over military and police that use violence to institute laws. It's purpose is to manage regions of physical land ('A State') for the purposes of economic exploitation by the elites. It maintains it's control by seizing monopoly control of important societial institutions such as court systems, police, national defense, financial systems (ie: money creation, banking regulation) and whatever else seems to be very important. The purpose of this is to allow more opportunity for profit and to make itself seem indespensible. It then uses laws and violence to protect it's position in these key areas.
State government cannot rule on violence alone. It needs the participation and at least some support among the general population. It does not produce any goods on it's own so it depends on the support of the 'people' to keep itself solvent. It depends on a combination of violence, propaganda, and such things to keep control.
To give some examples: United States Democratic Republic, Soviet Union, Modern democratic socialist countries in Europe, Fasicst Italian government, the kingdom of Saudi Arabia, Austrialian government, British Parlamentarian government, China's communist government, North Korean government, South Korean government, etc etc... These are all state governments. They are all essentially the same thing with the same patterns of behavior and control. There is differences in the severity and propagandic approaches they use, but when you look at them in terms of actual organization and how laws are enforced, how taxes are collected, how they regulate industry; they are almost identical.
Right now we live in a era were the state government is seen as indispensible as the Catholic church did to Christians the midevil times. During that era the idea of not having a Catholic church was a alien concept... it wasn't just unthinkable in a 'wow that is amazing' sense... it was simply something people didn't think about. The only alternative was paganism and damnation. They believed that without the church they would be lost and that they benefited from the church's control over their lives. (this changed with the protestant revolution and religious identity continues to evolve to this day)
That is how people feel about State Government right now. It's just not one way of having a government.. it is simply synonimous with government. The only alternative is 'Without Rule of Law'... which is means that you have chaos, people marrying dogs, roving bands of warlords, nobody can no longer get food or water, etc etc.
This, of course, is nonsense.
There are many other different forms of government. The Northern American Indians, for example, had money and trading. They produced goods specifically for trading using tools obtained from trading, which is the most basic definition of capitalism. They had common languages developed for economic interaction, they had laws, and all sorts of stuff like that. But they did not have state government.
To this day there are still remote areas of central and eastern Asia were there really is no effective form of state government. When you look on the map you will see state government borders and names of countries, but the people living there simply remain unaffected by them.
There are many potential ways for people to organize and govern themselves without depending on a monopoly services backed by violent central government.
In the imaginary Ancapistan people would be free to choose what form of government they want to use. No long would their be monopolistic control over important societal institutions, but competing agencies and approaches.